1. Introduction
Due to an increase in heat accumulation for ad- vanced electronic devices, there is an increasing de- mand for the fabrication of thermally conductive ma- terials that can be used to dissipate the heat generated by these devices. Heat accumulation is a huge prob- lem in advanced electronic devices as it reduces the lifetime and affects the reliability of the electronic devices [1]. For example, electronic devices with a high power density, such as LED lights and electron- ic speed controls, often undergo premature failure as a result of overheating [2]. In the past, polymer ma- terials were used as thermal management materials
due to their ease of processing, lightweight, low price, and electrical insulation [1–3]. However, the major drawback with polymers is their low thermal conductivities [1, 2, 4] (Table 1). In order to compen- sate for the low thermal conductivity of the poly- mers, conductive fillers are incorporated into the poly- mer matrix [1–4]. Figure 1 below shows the number of publications on boron nitride composites from 2015 to date. An increase in the number of publica- tions from 2015 to 2020 is observed from the bar graphs shown in Figure 1 below. This is because of the increasing severity of the heat accumulation prob- lem in the electronic devices produced nowadays,
Mechanical properties, thermal conductivity, and modeling of boron nitride-based polymer composites: A review
T. E. Mokoena1, S. I. Magagula2, M. J. Mochane1*, T. C. Mokhena3
1Department of Life Sciences, Central University of Technology, Free State, Private Bag X20539, 9300 Bloemfontein, South Africa
2SUN ACE South Africa (PTY) LTD, 12 Innes Road, Jet Park 1459, Johannesburg, South Africa
3Nanotechnology Innovation Centre, Advanced Materials Division, Mintek, Randburg, South Africa
Received 1 May 2021; accepted in revised form 19 July 2021
Abstract.In the past, polymer materials have been used in electronic devices; however, the major drawback with polymers is their low thermal conductivity, i.e., 0.1–0.5 W/(m·K). Hence, researchers came up with the idea of incorporating conductive fillers into the polymer matrix in order to increase their thermal conductivity. Different conductive materials classified as carbon, metallic, and ceramic-based fillers have been used for this task. However, the drawback with carbon and metal- based fillers is that they reduce the intrinsic insulating properties of polymer materials. Recently, boron nitride (BN), a ce- ramic-based filler was selected as the conductive filler of choice due to its combined excellent thermal conductivity and electrical insulation as well as high breakdown strength. Due to differences in polarities, boron nitride and polymer matrices form a weak interfacial bond. Therefore, the weak interfacial bond is commonly improved by surface chemical modification of the boron nitride fillers. Furthermore, most of the theoretical models are used to predict the thermal conductivities of boron nitride-polymers composites fitted well with experimental data. This proved that the models could be used to predict the properties of boron nitride composites before their experimental data. The review paper discusses the effect of boron ni- tride orientation, nanostructures, modification, and its synergy with other conductive fillers on the thermal conductivity and mechanical properties of the polymer matrices.
Keywords:polymer composites, hybrid conductive fillers, thermal conductivity, conductive fillers, boron nitride https://doi.org/10.3144/expresspolymlett.2021.93
*Corresponding author, e-mail:mochane.jonas@gmail.com
© BME-PT
which forced researchers to investigate more on the thermal conductivity of polymer/boron nitride com- posites.
Conductive fillers can be classified as carbon, metal- lic, and ceramic-based fillers, as shown in Table 2.
Previously, carbon-based materials such as graphite, carbon fiber, carbon nanotubes, and graphene have been commonly used as thermally conductive fillers due to their high thermal conductivity [9]. However, the major drawback with the use of these conductive fillers is that the essential insulating property of the polymer matrix is reduced [9]. Recently, boron nitride (BN) has been selected as a thermally conductive filler of choice due to its combined excellent electri- cal insulation and thermal conductivity as well as high breakdown strength which are a result of its wide bandgap (~5.9 eV) [9, 10].
However, it has been realized that a poor dispersion of the BN within the polymer matrix had a negative impact on the thermal conductivity values of the re- sultant composite. Therefore, the thermal conductivity of boron nitride can be improved by chemical sur- face modification of the boron nitride filler [4]. The surface modification of the filler improves the disper- sion of fillers in the polymer matrix [3]. In a study by Xu and Chung [13], BN particles were effectively treated with acetone, acids (nitric and sulphuric acids), and silane. The thermal conductivity of the BN-epoxy Figure 1.Recent publications on boron nitride composites
from 2015 to date (This information was obtained from the web of science search query on this date 24-03-2021).
Table 1.Thermal conductivity values of selected polymers.
Table 2.Selected thermally conductive filler.
Polymers Thermal conductivity
[W/(m·K)] References
Low-density polyethylene (LDPE) 0.30
[5]
High-density polyethylene (HDPE) 0.44
Polytetrafluoroethylene (PTFE) 0.25
Polyimide (PI) 0.11
Polyvinyl chloride (PVC) 0.19
Poly(ethylene terephthalate) (PET) 0.15
Polypropylene (PP) 0.25 [6]
Cresol Novolac epoxy resin 0.15–0.25 [7]
Diglycidyl ether of Bisphenol-A (DGEBA) epoxy resin 0.20 [8]
Diglycidyl ether of terephthalylidene-bis-(4-amino-3-methylphenol
(DGETAM isotropic phase) epoxy resin 0.35 [8]
Diglycidyl ether of terephthalylidene -bis-(4-amino-3-methylphenol
(DGETAM liquid crystalline phase) epoxy resin 0.38 [8]
Fillers Group types Thermal conductivity
[W/(m·K)] References
Graphene Diamond
Carbon nanotubes (CNTs)
Carbon-based
4000–5000 2966
>3000>
[11, 12]
Copper (Cu) Aluminium (Al) Sliver (Ag)
Metallic
483 247 450 Aluminium nitride (AIN)
Boron nitride (BN) Silicon carbide (SiC)
Ceramic
320 320 270
composites reached a maximum value of 10.3 W/(m·K) at 57 vol% BN content with silane treatment of the BN fillers, which was higher than that of BN-epoxy composites (5.27 W/(m·K)) consisting of untreated BN fillers at the same filler content.
This proved that filler surface treatment is an effec- tive way of improving thermal conductivity. Without surface treatment, weak bonds would be formed at the interface between the polymer matrix and inorganic BN particles [1, 2]. In a polymer composite, a weak interfacial bonding limits the movement of energy from the matrix to the filler where it propagates the fastest [1, 13]. When BN fillers are silane treated, the interaction at the filler-polymer matrix interface is im- proved because silane makes it easier for the inorganic filler, (BN) to bond with the polymer matrix (epoxy resin) [2]. According to Zhang et al. [14], besides sur- face treatment, compatibilizers (such as maleic anhy- dride grafted polyethylene) can improve the interfa- cial interaction between a polyethylene matrix and hexagonal boron nitride and hence improve the ther- mal and mechanical properties of the composites.
Furthermore, filler geometry can also affect the ther- mal conductivity of polymer composites [2]. For ex- ample, a higher in-plane thermal conductivity has been obtained with platelet-shaped fillers as com- pared to equiaxial-shaped fillers. However, the platelet-shaped fillers produce conductive materials that are anisotropic. This is because, during process- ing, the platelets are preferentially oriented in the flow direction [2]. This review paper discusses the effect of BN content, orientation, surface modification, com- patibilization, and its synergistic effect with other fillers on the thermal conductivity and mechanical properties of polymer matrices. The paper further discusses different models for predicting the thermal conductivity of the BN/polymer composites.
2. History, structure, and properties of boron nitride
Boron nitride (BN) is a crystalline compound that is synthetically produced and is made up of equal amounts of nitrogen (N) atoms and boron (B) arranged in a honeycomb configuration [1, 10, 15, 16]. BN was first synthesized in the 1840s by a British chemist by the name of Balman [10]. In the synthesis procedure, Balman used molten acid and potassium cyanide as precursors for the synthesis of BN [10]. This opened up an enormous amount of investigations on the syn- thesis of different types of BN nanostructures [10].
Up to date, the most commonly used methods for the synthesis of BN are the high-temperature pressure method [17], chemical exfoliation method [18], freeze-drying method [19], chemical vapor deposition method [20], boron ink method [21], microfludiza- tion [22], and liquid-phase exfoliation method [23].
Figure 2 shows hexagonal boron nitride of various thicknesses synthesized via the chemical deposition method. The chemical deposition method shows that the thickness of h-BN is controllable by controlling the growth of its atomic layers.
Furthermore, BN has a structure similar to that of graphite in which the carbon atoms are replaced by alternating B and N atoms [15]. BN is found in three crystalline forms, namely: cubic BN (c-BN, similar to diamond), hexagonal BN (h-BN, a layered structure like graphite), and wurtzite BN (w-BN, analogous to Ionsdaleite) [10]. Amongst the three forms of BN, h-BN, an sp2-hybridized 2D-layered insulator, is a highly crystalline form of BN under standard condi- tions. In the BN crystal structure, the bonding between the alternating B and N atoms is governed by robust B-N covalent bonds, and the stacking between the 2D layers is governed by weak van der Waals forces [16, 25, 26]. When compared with the C–C covalent bond- ing nature of its counterpart, the B–N bonding nature of BN is partially ionic due to the fact that the N atom has a higher electronegativity compared to the B atom [10]. Consequently, the optical, electrical, and sub- stance properties of BN are not the same as those of graphite [10]. However, like most carbon materials, BN can also exist in several different nanostructures such as boron nitride nanotubes (BNNT), boron ni- tride nanosheets (BNNS), and boron nitride nanorib- bons (BNNR), [10]. Other boron nano structures in- clude boron nitride fullerenes, boron nitride nano - fibers (BNNF), and boron nitride nanopowders (BNNP), [10]. The synthesis procedures of these BN nanostructures have been extensively reviewed by Joy et al. [10]. As a filler material, BN has attracted enor- mous attention in both the scientific and engineering fields due to its fascinating properties such as excel- lent thermal conductivity, large energy band gap, ther- mal stability, chemical inertness, good resistance to oxidation, and significant mechanical properties [26–
28]. Most of these properties were found to be gov- erned by its atomic structure [10]. In addition, BN is a perfect insulator and therefore suitable for heat dis- sipation in electronic devices that require both elec- trical insulation and increased thermal conductivity.
3. Fabrication and resultant dispersion of boron nitride-based Polymer composites The morphology of polymer composites is influenced by several factors, which include filler content, prepa- ration methods, filler modification, compatibilizers, particle size, filler shape, and type of polymer matrix [2, 6, 14, 29–31]. The effect of filler content on the morphology of BN/polyethylene composites was re- ported by Ayoob et al.[31]. In this study, hexagonal boron nitride was added into the polyethylene matri- ces (i.e. LDPE and HDPE) at various filler contents, i.e., 2, 5, 10, 20, and 30 wt%. In this study, the type of boron nitride used was hexagonal boron nitride (h- BN). Scanning electron microscopy (SEM) images showed a uniform distribution of the h-BN in the polyethylene matrix. However, a lot of agglomeration was observed in nanocomposites consisting of more than 10 wt% h-BN. Furthermore, the incorporation of
h-BN into the polyethylene matrix led to a disor- dered morphology when compared with pure poly- ethylene. This effect became more pronounced with increasing h-BN content. Similarly, Yu et al. [30] re- ported on the effect of filler (h-BN) content for a sys- tem that included BN and cellulosic fiber. Micron- sized voids were observed between the cellulosic fiber matrix and BN filler particles. At a lower filler loading, the BN particles were more evenly distrib- uted on the cellulosic fiber matrix surface. The BN particles kept a certain distance from each other and rarely made contact. However, at higher BN filler loading, the micron-sized voids were gradually oc- cupied by BN particles. In this case, the BN particles made contact with each other along the cellulosic fiber matrix skeleton. The increased contact area be- tween the h-BN filler particles led to the formation of networks called heat conductive pathways in the Figure 2.Optical images of (a) bulk, (b) six-layer, (c) double-layer and (d) single-layer h-BN and (e–h) corresponding optical images of the different layered h-BNs grown on SiO2substrates (scale bar of images (e–h) is 2 mm); (i) SEM image of a few layered h-BN on Ni foil (left-hand-side image scale bar is 1 mm) and optical image of a few layered h-BN film on SiO2(right-hand-side image scale bar is 100 μm); (j) bulk highly crystalline h-BN star-like structures on Ni foil (scale bar is 100 μm) [24] (MDPI open access).
composite. These pathways were just the needed structures to reduce thermal resistance in the com- posite. It has been shown that the synergy of BN with other fillers and preparation methods used in the fab- rication of polymer composites can also influence their morphology. For example, Wie and Kim [32]
prepared raw BN (R-BN)/Epoxy, graphene oxide (GO)/R-BN/epoxy, and GO/polysilazane coated BN (P-BN)/epoxy composite films via solution mixing followed by solvent casting and then curing. The morphologies of the prepared composite films were studied using cross-sectional SEM microscopy. The SEM image of the raw BN (R-BN)/epoxy composite showed a distinctly layered morphology due to the downward diffusion of the high-density R-BN dur- ing the curing process (see Figure 3a). This occur- rence hinders filler dispersion in the matrix and neg- atively affects composite performance. Figure 3d shows the presence of numerous gaps around the fillers in the R-BN/epoxy composites. This was an indication of the poor wettability of the R-BN fillers.
These gaps may hinder the flow of heat, which may result in heat loss. However, as shown by Figure 3b, the introduction of GO into the composite during the preparation process improved the degree of BN filler dispersion in the epoxy matrix. This is because the well-dispersed GO prevented the downward diffu- sion of the BN fillers during the curing process and therefore improved the degree of BN dispersion in the matrix. However, Figure 3e shows that the incor- poration of GO did not improve interfacial adhesion in the epoxy composite. This problem was rectified
via the surface modification of BN, which provided structural similarity with the epoxy matrix, as shown by Figure 3c and Figure 3f.
In another study, Yang et al. [33] prepared polyeth- ylene hexagonal boron nitride (PE/h-BN) composite sheets with improved thermal conductivity by an- nealing a multi-layered structure of alternating high- density PE (HDPE)/h-BN composites and low-den- sity PE (LDPE) layers. In order to study the disper- sion of fillers during annealing, SEM was used.
Through SEM, the cross-sections of the multi-lay- ered sheets annealed at 200 °C for different times were studied. The SEM images of these multilayers sheets were also compared to the SEM images of multi-layered sheets consisting of h-BN particles randomly distributed in both HDPE and LDPE ma- trices. From the SEM images of the multi-layered sheets, it was observed that the shrinkage of the com- posite layers continuously occurred for 2 h (120 min) annealing time. In the unannealed multi-layered sheets, the h-BN platelets dispersed in the HDPE ma- trix were dispersed parallel to the interfaces between neighboring LDPE layers. After annealing for dif- ferent time lengths, the thickness of the h-BN/HDPE composite layers shrank, and the concentration of h- BN was increased with annealing time. After anneal- ing for 30 min, the composite layers of the multi-lay- ered sheet became significantly thinner than before.
As a result, the concentration of h-BN was signifi- cantly increased, and the fillers began to percolate. In- creasing the annealing time led to a further decrease in the composite layer thickness, and the contact area
Figure 3.SEM images of the cross-sectional area of the prepared BN/epoxy composites: (a) raw BN (R-BN)/epoxy composite (scale bar is 500 μm), (b) graphene oxide (GO)/R-BN/epoxy composite (scale bar is 500 μm), (c) GO/polysilazane coated BN (P-BN)/epoxy composite (scale bar is 200 μm), (d, e, f) are the corresponding magnified areas of the marked areas (in a yellow square) in (a, b, c) ((scale bar of (d) and (e) is 200 μm and scale bar of (f) is 100 μm) [32] (MDPI open access).
Table 3.Selective studies on preparation and morphology of boron nitride-polymer composites.
Polymer composites Filler content Mixing method Results discussed on morphology References BN/ABS,
BN/ABS/HDPE, BN/ABS/PE-g-MA com- posites,
ABS = Acrylonitrile buta- diene styrene,
HDPE = high density polyethylene,
PE-g-MA = maleic anhy- dride grafted polyethyl- ene
40 wt% of BN
particles Injection molding
– Scanning electron microscopy (SEM) images of fractured surfaces showed an even distribution of 40 wt% BN platelets in all samples consisting of ABS, ABS/HDPE, ABS/PE-g-MA matrices.
– Voids were observed in BN/ABS and BN/ABS/
HDPE composites. Cracks were also observed around the edges of BN particles, indicating weak interfaces.
– No voids were observed in BN/ABS/PE-g-MA composites indicating that maleic anhydride im- proved the adhesion between the matrix and BN particles.
0[2]
PP/micro-BN,
PP/nano-BN composites, PP = polypropylene, micro-BN = microsized boron nitride,
nano-BN = nanosized boron nitride
3, 6 and 9 wt%
of BN particles
Melt mixing of PP and BN fillers using a two-roll open mill and hot pressing.
– Pure PP fractured surfaces were smooth and those of PP/micro-BN composites were rougher with increasing filler content, indicating a stronger interfacial interaction between micro- BN and PP.
– Nano-BN particles were uniformly distributed in the PP matrix at various filler contents, indicating a good interfacial interaction.
– The nano-BN particles were extremely dispersed in PP as compared with micro-BN particles. All the nano-BN particles were isolated from each other and therefore did not make contact at 9 wt% filler loading. However, flaky micro-BN particles created many short lines in the PP/
micro-BN composites, which gradually connect- ed with increasing filler loading. This caused the formation of thermal paths, which improved thermal conductivity.
[29]
PE/BN, PE/K-BN,
PE/M-BN composites, PE = polyethylene, K-BN = KH550 treated boron nitride,
PE/M-BN = (PE + PE-g-MAH)/BN, PE-g-MAH = maleic anhydride grafted poly- ethylene,
KH550 = γ-aminopropyl- triethoxysilane
10 wt% BN par- ticles
Compounding of PE and BN particles in an internal mixer at 180 °C for 8 min, and rotation speed of 30 rpm.
– SEM images of fractured composite surfaces showed some BN aggregates in composites con- sisting of 10 wt% BN. However, reasonably uni- form dispersion and good distribution were ob- served for composites consisting of 10 wt%
M-BN and 10 wt% K-BN, which was an indica- tion that surface functionalization of BN particles and addition of PE-g-MAH can improve the dis- tribution of BN particles with less aggregation.
[14]
iPP/h-BN/MWCNTs and iPP/h-BN/GNPs compos- ites,
iPP = isotactic polypropy- lene,
MWCNTs = multi-wall carbon nanotubes, GNPs = graphene nanoplatelets
10, 20 and
30 wt% of BN Melt-mixing
– Even though thermally conductive networks were formed in iPP/h-BN composites at high h- BN particle contents, there were still lots of iso- lated h-BN particles in the composites. There- fore, incorporated MWCNTs or GNPs acted as
‘bridges’ to connect these isolated h-BN particles and then further improved the thermal conduc- tivity of the iPP/h-BN composites.
[34]
BN/EP composites, EP = epoxy
5 and 20 vol%
of h-BN or c-BN particles
Incorporation of various contents of surface-modi- fied hexagonal boron ni- tride (h-BN) and cubic boron nitride (c-BN) pow- ders to epoxy resin matri- ces
– The cross-sectional morphology of the compos- ite materials became increasingly rougher as their BN content was increased.
[35]
between fillers was increased, which favored the for- mation of percolated thermal conduction pathways.
In addition to that, an increase in annealing time also increased the orientation of h-BN in the HDPE ma- trix. At higher annealing times, the fillers in the com- posite layers were highly oriented, and the h-BN platelets were arranged parallel to the interfaces be- tween neighboring LDPE layers. However, the multi- layered control sheet in which the h-BNs were ran- domly distributed in both HDPE and LDPE matrices only showed a typical sea-and-island-like structure with no preferred orientation. Table 3 is a summary of different methods used in the fabrication of boron nitride-polymer composites, as well as the obtained morphological properties.
4. Selective polymer matrices for
fabrication of polymer/boron nitride (BN) composites
Nowadays, a lot of effort has been focused on improv- ing the thermal conductivity of the polymers using conductive fillers [10]. The aim of this section is to classify the different polymer matrices used in poly- mer/BN composites as well as the effectiveness of BN in different polymer matrices (Table 4). According to this section, the polymer matrices can be broadly classified into two groups (i.e., thermoplastics and thermosets). Based on Table 4 below, thermoplastics are the most utilized polymer group in the prepara- tion of boron nitride-polymer composites. Jing et al.
[36], used poly(vinyl alcohol) (PVA) as a polymer matrix to prepare biocompatible hydroxylated boron nitride/PVA interpenetrating hydrogels with enhanced mechanical and thermal properties for biomedical applications. This is because PVA-based hydrogels are considered good cartilage replacement materials due to their tissue-like viscoelasticity, excellent bio- compatibility, and high hydrophilicity. In another study, Fei et al. [37] used thermoplastic polyurethane (TPU) to prepare flexible polyurethane/boron nitride composites with improved thermal conductivity.
When compared with other polymer matrices, TPU was used because of its superior properties, such as excellent flexibility, elasticity, chemical resistance, abrasive resistance, good adhesion, and good phys- ical properties. Du and Cui [29] used polypropylene (PP) as a polymer matrix in the preparation of micro, and nano-sized boron nitride-filled polypropylene composites with enhanced heat dissipation ability.
Polypropylene was used as a polymer matrix because
it was considered a recyclable insulating material with excellent electrical insulating properties.
Table 4 below is a summary of some of the polymer matrices used in the fabrication of boron nitride- polymer composites, as well as the corresponding composite properties.
5. The effect of surface modification on the thermal conductivity of BN-polymer composites
Thermally conductive networks in BN-polymer com- posites depend on the contact area of fillers and how well the fillers (in this case BN) are dispersed in the polymer composites. These contact points between the filler (BN) particles are found to be favorable to increase the thermal conductivity of the composites.
Higher filler contents transfer energy more efficient when the contact area between the fillers is larger.
However, higher filler contents lead to the formation of voids and aggregates formed in the polymer com- posites [48, 49]. It is well-known that the conductive pathways are hindered by voids formed between the filler particles and polymer matrix, which results in difficulties for the conduction of heat. Therefore, the surface modification of inorganic BN particles has been found to be an effective method to enhance thermal conductivity and the interaction between the filler-polymer matrix [50, 51].
Many researchers have reported on the use of vari- ous surface treatment methods such as silane cou- pling agents, surfactants, titanate coupling agents, and inorganic coatings for enhancing the dispersion of the filler filler-polymer matrix contact and thus reducing the thermal resistance [7, 48, 52–55]. Silane coupling agents are found to be effective modifiers and are popular amongst surface treatment methods.
They contain different functional groups, which allow their molecules to bond with inorganic materials, thus making them useful for enhancing the interac- tion between the filler and polymer matrix [55].
Wie et al. [52] modified the surface of the boron ni- tride using polysilazane (PSZ) and (3-glycidy- loxypropyl) tri-methoxysilane (GPTMS) to enhance thermal conductivity. There was an improvement of the thermal conductivity to 7.014 W/(m·K) of the composites containing filler loading of 50 vol% PSZ- and GPTMS-coated BN materials. This value was approximately 50 times higher as compared to that one of neat epoxy. One can suggest that there was a tremendous improvement of thermal conductivity,
Table 4.Summary of some of the polymer matrices used during the fabrication BN based polymer composites/nanocom- posites.
Nanocomposites
Type of polymer (thermoset or thermoplastic)
Typical example of nanocomposites
Nanocomposite properties (thermal conductivity, mechanical, thermal stability
properties, etc.)
References
Poly(vinyl alcohol)
(PVA)/BN Thermoplastic
PVA/OH-BNNS hydrogels OH-BNNS = hydroxylated boron nitride nanosheets
The incorporation of 0.12 wt% OH-BNNS in a PVA matrix increased the thermal conductivity and diffusivity of the PVA/OH-BNNS hydro- gels by 5 and 15%, respectively.
[36]
Polyurethane/BN Thermoplastic
TPU/BN
TPU = thermoplastic polyurethane
Composite exhibited 1390% enhancement in thermal conductivity with the incorporation of 50 wt% BN.
[37]
Cellulose/BN Natural polymer
OH-BNNS/CNF multilayer films
CNF = cellulose nanofiber
There was a significant increase of in-plane thermal conductivity in the multilayer films, and the unit weight filler exhibited an increased thermal conductivity efficiency up to 1142%.
[38]
Polystyrene (PS)/BN Thermoplastic BNNS/PS nanocomposite
The 5:1 styrene:BN feeding ratio improved thermal conductivity values up to a maximum of 1375%.
[39]
Polypropylene (PP)/BN Thermoplastic, polyolefin
Micro- and nano-sized BN/polypropylene com- posites
The thermal conductivity was higher for micro- sized BN/PP composites as compared to that of PP/nano-BN composites at the same BN filler loading.
[29]
Polyacrylamide
(PAM)/BN Thermoplastic h-BN/PAM nanocomposite hydrogels
The incorporation of h-BN nanosheets im- proved the elongation at break of the h-BN/BN nanocomposite hydrogels up to 1000%. This signified that the interfacial interaction between the h-BN nanosheets and PAM matrix was strong. This strong interfacial bond can there- fore improve the thermal conductivity of the composites hydrogels.
[40]
Polycaprolactone (PCL)/BN
Thermoplastic, polyester
PCL/PLA blends incorpo- rated with h-BN nanoplatelets, PLA = polylactic acid
Adding the h-BN nanoplatelets increased the thermal conductivity of PCL/PLA blends by 400%.
[41]
Polyacrylonitrile/BN Thermoplastic Polyacrylonitrile/h-BN composites
At 10 wt% h-BN the composites had improved thermal stability (280 °C), higher ionic conduc- tivity (1.0·10–3S/cm), larger electrolyte uptake (1200%), and best electrochemical stability (4.7 V).
[42]
Acrylonitrile�butadi- ene�styrene (ABS) copolymer/BN
Thermoplastic ABS/h-BN, ABS/mBN, mBN = modified BN
The thermal conductivity of the ABS/mBN composite was improved 2.6 times more than pure ABS at 20 wt% mBN.
[43]
Epoxy/BN Thermoset
PCB-BN/epoxy, PCB-BN = polyphosp- hazene-coated BN
PCB-BN improves the thermal transport per- formance of epoxy resins. Thermal conductivity of 0.708 W/(m·K) at 20 wt% PCB-BN particle loading was observed. This was 3.7 times high- er as compared to that of pristine epoxy.
[44]
Polyimide (PI)/BN Thermoset PI/micro-BN and PI/nano-BN
Composites consisting of 30 wt% micro-BN and nano-BN at a 7:3 PI:BN ratio showed the highest thermal conductivity.
[45]
BN-c-MWCNT/PI films, BN-c-MWCNT = Boron nitride coated multiwalled carbon nanotubes
The thermal conductivity of films consisting of 30 wt% BN-c-MWCNTs was enhanced by 106%.
[46]
Cyanate ester/BN Thermoset Cyanate ester/silane cou- pling agent modified BN
The incorporation of 23.6 wt% BN increased the thermal conductivity of the composite to 1.33 W/(m·K), which was 4.6 times more than that of the present matrix.
[47]
which was attributed to the treated surface of boron nitride using two-step surface modification. This in- dicated that their methods were more effective for enhancing thermal conductivity in comparison to other reported studies on BN-polymer composites.
Chung and Lin [7] studied the thermal conductivity of epoxy composites filled with synthesized h-BN particles. The h-BN surface was treated with 3-gly- cidoxypropyltrimethoxysilane (GPTMS). It was re- ported that the GPTMS reduced the voids and thermal barrier between the filler and matrix, which resulted in a slight increase in thermal conductivity from 15.1 to 20.3% as a result of GPTMS surface treatment.
Furthermore, Lee and Kim [56], used a one-step ex- foliation and functionalization method to prepare an amine-group functionalized hybrid filler consisting of boron nitride and aluminum nitride (BA-NH2).
The hybrid filler (BA-NH2) and a cellulose nanofiber (CNF) were used to prepare a thermally conductive film (CNF/BA-NH2) via vacuum filtration and hot- press processing. After surface treatment of each filler in the hybrid filler, the dispersion of the hybrid filler in the film matrix was improved. This was due to hydrogen bonding interactions which improved the interfacial adhesion between the filler and ma- trix. Furthermore, treated aluminum nitride particles deposited on surface-treated BN particles promoted the formation of heat transfer paths along the through- plane direction. The thermal conductivity was in- creased from 0.5 W/(m·K) (neat CNF film) to 5.93 W/(m·K) (at 50 wt% BN filler content), which was a 1092 % increase compared with the neat CNF film. Table 5 illustrates a summary of the selective studies on the thermal conductivity of BN-polymer composites.
6. Thermal conductivity of the boron nitride-hybrid composites
Recently, several researchers have shown a tremen- dous interest in the incorporation of thermally con- ductive mixed fillers (hybrid fillers) into polymer matrices as a means of improving the low thermal conductivity of polymers [62–66]. The hybrid con- ductive fillers are easily dispersed in the polymer matrix, and therefore they reduce the amount of voids in the matrix [67]. Methods such as simple mixing with a paste mixer, direct blending, physical adsorption, chemical bonding, and hot-pressing are some of the methods used for the preparation of hy- brid thermally conductive composites. Methods such
as the direct blending method are suitable for use when thermally conductive fillers with different sizes are involved. This method mainly focuses on the spatial matching of thermally conductive fillers with different sizes [62, 67, 68]. Jiang et al. [69] pre- pared functionalized graphene (GR)-boron nitride (BN)-polystyrene (PS) composites by solution blend- ing. It was reported that the thermal conductivity of the GR-BN-PS composites reached the maximum of 0.24 W/(m·K) which was slightly higher than that of GR-PS composites (0.22 W/(m·K)) and the pure PS (0.15 W/(m·K). In order to understand the effective- ness of conductive hybrid fillers, thermal enhance- ment (ϕ) parameters and synergistic efficiency (f) are used to estimate the degree of thermal conductivity enhancement in the composites and they are ex- pressed by Equation (1) and (2):
(1) where λcomand λPrepresents the thermal conductiv- ity of polymer-based composites and pure polymer samples, respectively.
(2) where λsefcrepresents the thermal conductivities of the synergistic effect of two fillers in the composites, λf1and λf2represents the thermal conductivities of the two fillers in the composites [6, 70]. A high value of f(>1) means that there is a high probability of ob- taining higher thermal conductivity and vice versa [6]. Yang et al. [70] incorporated graphene nano - platelets (GNPs) into poly (ethylene glycol) (PEG)/
boron nitride (BN) composite phase change materi- als (PCMs). The results revealed that the thermal en- hancement (ϕ) of the PEG/BN/GNP PCM composites was enhanced with the incorporation of 1 wt% GNP content. It was also observed that the synergistic ef- ficiency (f) increased with increasing BN content which was higher than 1 for all the PEG/BN/GNP composites PCMs. This indicated that there was an increase in the synergistic efficiency of BN and GNP with an increasing BN content. In another study, Wu et al. [71] investigated the synergistic effects of boron nitride Nanosheets (BNNSs) and silver (Ag) nano - particles on the thermal conductivity and electrical properties of epoxy (EP) Nanocomposites. The epoxy nanocomposites consisting of a hybrid nano filler were denoted as EP-AgBN, and those without a hybrid
%
P 100
com P $ z= m m-m
f f1 P f2 P sefc P
m m m m
m m
= - + -
-
R W R W
nanofiller were denoted as EP-BN. Thermal conduc- tivity results showed the thermal conductivity of the EP-AgBN composites was greatly improved at high- er nanofiller loadings (beyond 10 vol%) as compared to that of EP-BN composites (see Figure 4a). A sim- ilar observation was also made with the thermal con- ductivity enhancement (TC-E) of the composites
at higher nanofiller loadings (see Figure 4b). The thermal conductivity of EP-AgBN reached a maxi- mum value of 2.14 W/(m·K) at a filler loading of 25 vol%, which was almost twice that of EP-BN (1.13 W/(m·K)). This indicated that the AgNPs- BNNS nano-hybrid filler improved the thermal con- ductivity of epoxy more that the BNNS nanofiller.
Table 5.Summary of selective studies on the thermal conductivity of BN-polymer composites.
Composites system Filler or fillers Technique used to enhance thermal conductivity
Discussions and thermal conductivity of the composites
[W/(m·K)]
References
Surface treated boron ni- tride (BN)/epoxy-terminat- ed dimethylsiloxane (ETDS) composites
BN,
surface-treated BN
The sol-gel method was used to modify BN particles with silica using tetraethyl orthosilicate (TEOS).
The thermal conductivities of surface-modi- fied BN/ETDS composites ranged from 0.2 to 3.1 W/(m·K) which were above those of unmodified BN/ETDS composites at the same filler content.
[53]
h-BN-KH550/polytetraflu- oroethylene (PTFE), h-BN/PTFE composites
h-BN, h-BN-KH550
h-BN platelets were treated with a silane coupling agent (KH550)
h-BN surface modification improved inter- facial adhesion between h-BN platelets and PTFE matrix and reduced the in-plane orien- tation degree of h-BN platelets in the PTFE matrix, which consequently enhanced the thermal conductivity of the composites. The thermal conductivity of h-BN-KH550/PTFE composites reached 0.722 W/(m·K) at 30 vol% filler content, which was 2.7 times that of pure PTFE.
[57]
Functionalised-BN (f-BN)/polyimide compos- ites
BN, f-BN
Functionalization of boron ni- tride surfaces with γ-glyci- doxypropyltrimethoxysilane (KH-560) and aminopropy- lisobutyl polyhedral oligomeric silsesquioxane (NH2-POSS).
f-BN/PI composites exhibited a thermal con- ductivity coefficient of 0.71 W/(m·K) at 30 wt% f-BN, which was higher than that of BN/PI composites at 30 wt%
(0.69 W/(m·K)).
[58]
Boron nitride/cellulosic
fiber insulating composites h-BN
Grafting of (3-aminopropyl) tri- ethoxysilane (APTES) onto the surface of h-BN fillers and in- corporation of dual-sized fillers.
APTES grafting and incorporation of dual- sized fillers enhanced the thermal conductiv- ity of composites significantly. The thermal conductivity of composites with dual-sized surface-modified BN fillers reached 0.68 W/(m·K) at 41.08 wt% h-BN loading, which was 387% more than that of pure cel- lulosic fiber.
[30]
Polyimide (PI)/amino-BN, PI/BN-ND,
Amino-BN = h-BN with amino groups attached to its surface,
BN-ND = h-BN nanodia- mond hybrid filler
h-BN, BN-ND hybrid filler.
Amino group functionalization of h-BN and fabrication of a nano-micro hybrid filler con- sisting of h-BN and nanodia- mond.
Both surface modification of h-BN fillers and incorporation of hybrid fillers improved the thermal conductivity of composites. The highest thermal conductivity of the compos- ites was 0.98 W/(m·K) (5.2 times that of PI).
It was achieved by incorporating 40 wt% hy- brid filler (in a 1:10 ratio of ND: modified BN).
[59]
High-density polyethylene (HDPE)/hexagonal boron nitride (h-BN) nanocom- posites
h-BN
Surface modification of hexag- onal boron nitride nanoparticles (h-BN) via treatment with cold ethylene plasma.
Generally, all HDPE/h-BN nanocomposites exhibited improved thermal conductivities when compared with pure HDPE. Plasma treated samples (treated at 100 W for 5 min) exhibited conductivity values that were 97 and 114% higher than that of pure HDPE at 8 wt% and 15 wt% h-BN content.
[60]
Epoxy resin-impregnated insulation paper (RIP) com- posites modified with nano-h-BN
Nano-hexago- nal boron nitride (nano- h-BN)
RIP composites were modified with nano-h-BN
A maximum heat conductivity of 0.478 W/(m·K) was reached with nano-h-BN modified RIP composites, which was 139%
more than that of unmodified RIP compos- ites.
[61]
Furthermore, a similar study by Zhang et al. [72] in- vestigated the synergistic efficiency of positively charged boron nitride (pBN) and negatively charged carbon nanotubes (nCNTs) hybrid fillers incorporat- ed into a high-performance epoxy (EP) matrix. The results revealed that the thermal conductivity of pBN@nCNTs/EP composites could reach a value of 1.986 W/(m·K) with 50 wt% filler loading at a 10:1 mass ratio of pBN:nCNTs, which was 464 and 124%
higher than that of pure EP and BN/EP, respectively.
This indicated that the incorporation of nCNTs par- ticles into BN/EP composites was effective in in- creasing the thermal conductivity of the composites.
Furthermore, the overall synergistic efficiency of the composites was larger than 1 (f> 1), which demon- strated an excellent synergistic effect of the nCNTs and pBN hybrid fillers in improving the thermal con- ductivity of the composites. The synergistic efficiency decreased with the increasing mass ratio of nCNTs and pBN hybrid fillers. This was attributed to the
smaller content of carbon nanotubes in the co-fillers, which resulted in the isolation of some pBN fillers in the matrix. It is well-known that mixing different sizes (nano and micro or nanowire and nanosheets) of thermally conductive fillers can increase the prob- ability of forming thermally conductive pathways.
This is because the small-sized fillers can fill the gaps between the large-sized fillers, and the small nano - sheets can be packed between the nanowires [69].
For example, Wu et al. [74] prepared thermally con- ductive ternary poly(vinylidene fluoride) (PVDF)- based dielectric materials via the engineering of the filler networks of hexagonal boron nitride (h-BN) nanosheet and surface functionalized silicon carbide (f-SiC) nanowires. The synergistic effect of the h-BN nanosheets and f-SiC nanowires enhanced the ther- mal conductivity of the composites. This is because the parallel-oriented f-SiC nanowires were bridged by h-BN nanosheet networks. The highest thermal con- ductivity reached was 1.41 W/(m·K) which 5.9 times Figure 4.(a) Thermal conductivity versus nanofiller content plot of epoxy (EP)-boron nitride (BN) and epoxy (EP)-silver nanoparticle modified boron nitride (AgB) and (b) thermal conductivity enhancement(TC-E) versus nanofiller content plot of EP-BN and EP-AgBN [71] (MDPI open access).
Figure 5.Thermally conductive pathways of polymer nanocomposites (a) with no inter-filler networks and (b) consisting of inter-filler networks [71] (MDPI open access).
that of neat PVDF. This thermal conductivity was achieved with ternary blends consisting of 20 wt%
h-BN nanosheets and 26 wt% f-SiC nanowires. In another study, Wu et al. [71] illustrated the formation of thermal pathways between silver nanoparticles (AgNPs) and boron nitride nanosheets (BNNSs) in an epoxy nanocomposite (see Figure 5). The illustration
showed that the main thermal transfer paths were formed by BNNSs in the nanocomposites and the AgNPs connected the BNNSs as a ‘thermal bridge’, which resulted in the formation of inter-filler thermal networks in the polymer composites. Nanocompos- ites consisting of the inter-filler networks had a high- er thermal conductivity than those without a network.
Table 6.Selective studies on the hybrid fillers for enhancing the thermal conductivity of the composites.
Composites system Hybrid fillers Effect of hybrid fillers on thermal conductivity of the composites
[W/(m·K)] References
Boron nitride nanosheets (BNNs)- graphene nanosheets (GNs)-poly - tetrafluoroethylene (PTFE) compos- ites
BNNs and GNs
The results revealed that the thermal conductivity of the BNNs-GNPs- PFTE composites reached a value of 1.41 W/(m·K) which was higher than that of BNNs-PFTE composite (0.74 W/(m·K) and PFTE poly- mer (0.32 W/(m·K) at the same filler content (BNNs-24 wt% and GNPs-1 wt%). This indicated that the incorporation of even a small content of GNPs (1 wt%) into the BNNs-PFTE composites signifi- cantly improved the thermal conductivity of the composites.
[73]
Epoxy (EP)-boron nitride-silver
(AB) nanocomposites Ag and BN
The nano-hybrid filler loading of 25 vol% significantly increased the thermal conductivity of the EP-AB nanocomposites to 2.14 W/(m·K).
This improvement was due to the silver bridge connection between the boron nitride nanosheets (BNNS) and, thus, forming the thermal conduction channels in the composites.
[74]
Ultra-high-molecular-weight poly - ethylene (UHMWPE)/boron nitride particle (BNp), boron nitride sheet (BNs), and UHMWPE/
(BN+MWCNT) hybrid filler com- posites
BNp, BNs and MWCNTs
The thermal conductivity of the UHMWPE/(BNs+MWCNT) com- posite was increased to 1.641 W/(m·K), and that of the UHMWPE/
(BNp+MWCNT) composite was also increased to 1.533 W/(m·K) at 50 wt% hybrid filler loading.
[63]
Cellulose nanofibers (CNFs)/boron nitride nanotubes (BNNTs) compos- ites
BNNTs and Ag
The thermal conductivity of the Ag-BNNTs/CNF was higher than that of the BNNTs/CNF composites. For instance, at 25 wt% BNNTs load- ing, the thermal conductivity of the Ag-BNNTs/CNF composites was 20.9 W/(m·K) whilst that of the BNNTs/CNF composites was 12.9 W/(m·K).
[68]
Boron nitride (BN)/multi-walled carbon nanotubes
(MWCNTs)/polyphenylene sulfide (PPS) composites
BN and MWCNTs
It was reported that the thermal conductivity of the BN-MWCNTs- PPS composites was almost the same as that of BN/PPS composites.
This indicated that the synergistic effect between the BN and MWCNTs was not effective with the melt-mixing method.
[75]
Micro-boron nitride/nano-Al2O3/ epoxy composites (micro-nano- composites)
Micro-BN and nano-Al2O3
The thermal conductivity of the hybrid composites reached a value of 1.182 W/(m·K) with 22.5 wt% BN and 7.5 wt% Al2O3, which was 700% higher than that of a neat epoxy resin (0.148 W/(m·K))
[76]
Boron nitride/aluminium nitride
(AlN)/epoxy composites BN and AIN
The thermal conductivity of hybrid composites reached a value of 2.4 W/(m·K) at 40% hybrid BN-AIN filler contents, which was much higher than that of BN/EP (1.3 W/(m·K)) and AlN/EP composites (1.4 W/(m·K)), respectively. This high enhancement of the thermal conductivity was attributed to the synergistic effect of BN and AlN particles.
[77]
Boron nitride nanosheets
(BNNS)/graphene oxide nanosheets (GO)/poly(vinyl alcohol) (PVA) composites
BNNS and GO
The incorporation of 0.8 wt% GO particles in the PVA/0.8BNNS com- posites improved the in-plane thermal conductivity to 9.90 W/(m·K) which was approximately 38 times that of the cross-plane conductiv- ity. The GO nanosheets improved the distribution of the boron nitride nanosheets, which resulted in the significant enhancement of in-plane thermal conductivity.
[78]
Boron nitride/aluminium
nitride/ultra-high multi weight poly- ethylene (UHMWPE) composites
BN and AIN
The thermal conductivity of the segregated hybrid fillers (BN+AIN)/
UHMWPE composite reached a value of 6.44 W/(m·K) at the ratio of 3:1 BN: AIN, which was 23 and 321% higher than that of individual filler composites (BN/UHMWPE composite and AIN/UHMWPE composite) at 50 wt% filler content. This observation showed that the low thermal conductivity of pure UHMWPE polymer (0.39 W/(m·K)) was successfully enhanced more with the incorporation of hybrid fillers (BN+AIN) than with individual fillers.
[64]
This is because the inter-filler contact resistance is less than the interfacial thermal resistance between matrix and filler. Table 6 summarizes the selective studies on the incorporation of conductive hybrid fillers into polymer matrices for enhancing the ther- mal conductivity of BN-polymer composites.
7. The effect of orientation of boron nitride on the thermal conductivity of the
composites
It has been observed that the orientation of fillers has an effect on improving thermal conductivity and forming excellent thermally conductive networks [79–83]. Controlling the orientation of fillers in a polymer matrix is crucial for increasing the thermal conductivity enhancement of composites [83]. Liu et al.[79] investigated the thermal conductivity of random and oriented BN/PDMS composites as well as the thermal conductivity of random and oriented boron nitride (BN)/alumina (Al2O3)/ polydimethyl- siloxane (PDMS) composites. The thermal conduc- tivity of the oriented composites is aniso tropic. The results obtained by Liu et al.[79] were focused on the thermal conductivity of composites oriented in the in-plane orientation direction. It was reported that the filler oriented-BN/ PDMS and oriented- BN/Al2O3/PDMS composites exhibited slightly high- er thermal conductivities in comparison to random BN/PDMS and random BN/Al2O3/PDMS compos- ites, indicating that the in-plane orientation of the BN fillers improved the thermal conductivities of the polymer composites. Furthermore, it was also report- ed that the in-plane orientation of hybrid fillers great- ly improved the thermal conductivity of the compos- ites as compared to the in-plane orientation of
individual fillers. Song et al. [66] investigated the synergistic effects of different ceramic fillers on ther- mally conductive polyimide composite films. The thermally conductive composite films were prepared using an anisotropic boron nitride (BN) and hybrid filler system combined with spherical aluminum ni- tride (AlN) or aluminum oxide (Al2O3) particles in a polyimide matrix. The hybrid system led to a de- crease in the through-plane thermal conductivity and an increase in the in-plane thermal conductivity of the BN composite. The highest values were recorded along the in-plane direction of the films containing hybrid fillers as shown in Figure 6. This was ascribed to the horizontal alignment and anisotropy of BN.
Chen et al. [82] prepared boron nitride nanosheets (BNNS)/cellulose nanofiber (CNF) shear-oriented and self-oriented film composites. It was reported that the in-plane thermal conductivity of BNNS/CNF shear-oriented films at 50 wt% filler loading was en- hanced to 24.66 W/(m·K) as compared to that of pure CNF polymer (2.04 W/(m·K)). However, for the self-oriented films, the thermal conductivity was im- proved to 8.61 W/(m·K) at the same filler loading.
This indicated that the shear-oriented films gave bet- ter results compared to self-organized films. Cao et al.[81] investigated the thermal conductivity of the oriented-BNNs/polyimide (PI) composites. The ther- mal conductivity of oriented-BNNs/PI composites at filler loading of 12.4 vol% BNNs was significantly increased to 4.25 W/(m·K) as compared to that of pure PI polymer (0.85 W/(m·K)) and random- BNNs/PI composite (1.3 W/(m·K)). This indicated that the thermal conductivity of oriented-BNNs/PI composites increased by 69 and 80% as compared to the thermal conductivities of random-BNNs/PI
Figure 6.Thermal conductivity versus filler content plots of the composite films obtained along the (a) through-plane and (b) in-plane directions [66] (MDPI open access).
composites and pure PI polymer. Kim and Kim [83]
investigated the use of an external magnetic field to induce vertical filler alignment along the direc- tion of heat transport in boron nitride/epoxy com- posites. The thermal conductivity of the vertically aligned BN-EP composites was significantly in- creased from 1.765 to 3.445 W/(m·K) at 30 vol%
filler loading. This was a 1.96-fold increase when compared to the thermal conductivity of random BN-EP composites.
8. Modeling of thermal conductivity of boron nitride-polymer composites
Due to the increasing demand for high thermal con- ductivity materials in thermal management applica- tions, numerous models such as Maxwell model, Rayleigh model, McKenzie model, Bruggeman model, Hashin-Shtrikman model, Voigt-Reuss (series and parallel model), modified effective medium ap- proximation (EMA) model, Lewis-Nielsen model, and Agari model have been used over the years to predict the thermal conductivity of the fabricated BN- polymer composites and their conductive hybrid com- posites [9, 14, 58, 73, 84–88]. Combining experimen- tal data and theoretical calculations (models) is nec- essary because it makes it easier to understand and analyze the effectiveness of the thermal conductivity in polymer composites. For example, Cai et al. [73]
used the modified effective medium theory (EMT) to analyze the synergistic effect between GNs and BNNs on the thermal conductivity of the compos- ites. The used EMT model took into account factors such as the filler size and orientation as well as the thermal resistance at the filler-matrix interface. The effective thermal conductivity (Keff) of the boron ni- tride–polytetrafluoroethylene (PTFE) (BP) compos- ites was calculated using Equation (3):
(3) where according to the authors, Kmrepresented the thermal conductivity (TC) of the matrix. fBNrepre- sented the BNNs filler content. fCrepresented the critical filler content which is equal 0.001. The pa- rameter, ttrepresented filler dispersion in the PTFE matrix. t= 1 means that the filler is dispersed ran- domly in the matrix, and t> 1 means that the filler is inhomogeneously dispersed in PTFE. Generally, when the value of tis increased, the filler dispersion
in the matrix becomes worse. The reasonable bounds for parameter twould be 1 <t< 2. The EMT model suggests that improving the value of t and reducing thermal resistance (RK) at the filler-matrix interface facilitates phonon transmittance and hence improves the effective thermal conductivity (Keff).
When hybrid fillers such as BNNs and GNs were taken into account, the EMT equation in Equation (3) was changed by the authors to the Equation (4):
(4) where according to the authors, fGNs represented GNs content. KBNeffand KGNseff
represented the effective TCs of BNNs and GNs in the PTFE matrix. KBNeffand KGNseff
are defined by the Equations (5) and (6):
(5)
(6) where according to the authors, KBNand KGNsrep- resented the TCs of BNNs and GNs. lBN and lGNs
represented the lengths of BNNs and GNs, which can be obtained from SEM images. RKrepresented thermal resistance at the fillers-PTFE matrix.
In this study, the tand RKvalues in Equations (3) and (5) were set as 1.43 and 7·10–8m2·K/W for BP com- posites. It was observed by the authors that the exper- imental thermal conductivity values of the BP com- posites fitted well with their theoretical values. For BGP composites, the tand RKvalues in Equations (4) and (6) were also like those of BP composites. At these values, the theoretical thermal conductivity val- ues of the BGP composites agreed well with the ex- perimental values. However, when the filler content was above 10%, the theoretical values were much less than the measured values. Similar observations were reported by Goldin et al. [86] when using three mod- els (Maxwell, Lewis-Nielsen, and Agari-Uno) to in- crease the thermal conductivity of photopolymeriz- able composites. Both models (Lewis-Nielsen and Agari-Uno) fitted well with the experimental results, providing a much more improved thermal conductiv- ity, whereas the Maxwell model was ineffective be- cause the predicted values of thermal conductivity were much less in comparison with experimental re- sults. Song et al. [66] used the Lewis-Nielsen and
K K f
f f
3
3 2 t KK
eff m BN
BN C BNm
eff
= -
+ R - WS X
K f f
f f f
3
3 2 t 2
BN K K
K K
eff GNs
BN C BNm GNs
eff
m GNseff
= - +
+ R - +
R
S S
W X
W
X
K K
l 1
R K 2
BNeff BN
BN K BN
= +
K K
l 1
R K 2 GNseff GNs
GNs K GNs
= +
modified Lewis-Nielsen theoretical prediction mod- els to predict the in-plane thermal conductivity be- havior of thermally conductive polyimide (PI) com- posite films. A perfect fit between the experimental and theoretical data in both models was only ob- tained for the single-filler system using BN (PI/BN) (Figure 7). The other composites showed underesti- mated values (see Figure 7).
Furthermore, in another study by Pan et al. [84] the effect of h-BN’s anisotropy in h-BN/PTFE compos- ites was analyzed using the Maxwell model. It was reported that when the filler loading was below 20 vol%, the experimental thermal conductivity was basically the same as the predicted values by the Maxwell model (through-plane), showing that there was a good agreement between the two results.
However, at higher filler loading above 20 vol%, the effective experimental thermal conductivity was in- creased rapidly, showing higher values compared to predicted values by the Maxwell model (in-plane).
Therefore, this proved that the measured experimental
thermal conductivity gave better results compared to predicted values by the Maxwell model (in-plane and through-plane). However, when the modified ef- fective medium approximation (EMA) model was used, the effective thermal conductivity of randomly oriented h-BN was much higher than the measured experimental values. Zhang et al. [14] used the Agari model to predict the thermal conductivity of PE/BN composites. There was an increase in thermal con- ductivity due to the formation of a thermally con- ductive network formed by fillers with respect to the Agari model’s results. The modification of BN sur- face particles and the incorporation of a compatibi- lizer (i.e., PE-g-MAH) also contributed to the build- ing of thermally conductive pathways. However, the incorporation of the compatibilizer was found to be more effective in enhancing the thermal conductivity than the modification of BN surface particles. The comparisons between experimental results and the- oretical models of selected studies on BN-polymer composites are summarized in Table 7.
Figure 7.Experimental and theoretical thermal conductivity predicted with the regular and modified Lewis-Nielsen models for the (a) polyimide (PI)/BN; (b) PI/(aluminum oxide) Al2O3; and (c) PI/(aluminum nitride) AlN composite films [66] (MDPI open access).
